This paper introduces a new type of polynomials generated through the convolution generalized multivariable Hermite and Appell polynomials. The explores several properties these polynomials, including recurrence relations, explicit formulas using shift operators, differential equations. Further, integrodifferential partial equations for are also derived. Additionally, study showcases practical ...

In this paper, we introduce a new class of generalized extended Laguerre-based Apostol-type-Bernoulli, Apostol-type-Euler and Apostoltype-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite Bell-Hermite find representations. We derive some implicit summation formulae symmetric identities for these families special functions by applying the generating functions.

The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials. Expansions in terms of orthogonal polynomials are very common in many applications. While the connection problem may be solved by directly computing the change–of–basis matrix, ...

The monomiality principle was introduced (see e.g. [1] and the references therein) in order to derive properties of special polynomials from the corresponding ones holding for monomials. A set of paramount importance in this framework is given by the Hermite-Kampé de Fériet (shortly H-KdF) or Gould-Hopper polynomials [2], [3], [4]. As it is well known, the Hermite-Kampé de Fériet polynomials H ...

The object of this paper is to prove combinatorially several (13 of them) limit formulas relating different families of hypergeometric orthogonal polynomials in Askey’s chart classifying them. We first find a combinatorial model for Hahn polynomials which, as pointed out by Foata at the ICM (1983), “contains” models for Jacobi, Meixner, Krawtchouk, Laguerre and Charlier polynomials. Seven limit...

the gravity recovery and climate experiment (grace), twin satellites launched in march 2002, are making detailed measurements of the earth's gravity field. it will yield discoveries about gravity and the earth's natural systems. different sensors and instruments have been placed in the grace satellites to fulfill the primary scientific objective of the mission in mapping the earth’s g...